There are many studies on hydration of acetylene compound (e.g., Non-Patent Documents 1 to 3). However, the hydration is performed in the presence of mercury catalysts, which are harmful for humans and environment. It has not been reported that keto acids and keto acid derivatives (keto esters and the like) are synthesized from acetylene compound.    [Non-Patent Document 1]
R. C. Larock et al. “In Comprehensive Organic Synthesis” Ed. 1991, 4.269    [Non-Patent Document 2]
J. March. “Advanced Organic Chemistry”, 1992, 762    [Non-Patent Document 3]
M. Beller et al. Angew. Chem., Int. Ed. 2004 43, 3368
The object of the present invention is to provide a method for synthesis of keto acids (including keto acid and keto acid derivative) by hydration of acetylene-carboxylic acids under mild conditions free from any harmful mercury catalysts. Further, the object of the present invention is to provide a method for synthesis of amino acids (including amino acid and amino acid derivative) from acetylene-carboxylic acids in a single container (one-pot or tandem synthesis) by sequentially performing hydration of acetylene-carboxylic acids and reductive amination of keto acids (including keto acid and keto acid derivative).